My maternal grandfather traveled with an uncle from Russia to Ellis Island. Family lore has it that they were separated before disembarkment, so my grandfather lied about his age to make himself old enough to enter the country on his own.  Like many, he actually didn't know his birthdate, only that it was Passover of a certain year in the 1890s. 

My paternal grandfather brought several younger siblings from Russia to Ellis Island. He was about 17-18 at the time.  His siblings were about 9 or 10 years old. 

From this anecdotal history, I conclude that there was a minimum age for children traveling alone, but not for those traveling with adults. 
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Barbara Sloan
Conway, SC